Bayesian Dyadic Trees and Histograms for Regression
Authors: Stéphanie van der Pas, Veronika Ročková
NeurIPS 2017 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this work, we shed light on the machinery behind Bayesian variants of these methods. In particular, we study Bayesian regression histograms, such as Bayesian dyadic trees, in the simple regression case with just one predictor. We focus on the reconstruction of regression surfaces that are piecewise constant, where the number of jumps is unknown. We show that with suitably designed priors, posterior distributions concentrate around the true step regression function at a near-minimax rate. These results do not require the knowledge of the true number of steps, nor the width of the true partitioning cells. Thus, Bayesian dyadic regression trees are fully adaptive and can recover the true piecewise regression function nearly as well as if we knew the exact number and location of jumps. Our results constitute the first step towards understanding why Bayesian trees and their ensembles have worked so well in practice. |
| Researcher Affiliation | Academia | Stéphanie van der Pas Mathematical Institute Leiden University Leiden, The Netherlands svdpas@math.leidenuniv.nl Veronika Roˇcková Booth School of Business University of Chicago Chicago, IL, 60637 Veronika.Rockova@Chicago Booth.edu |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any explicit statements about releasing source code or links to a code repository. |
| Open Datasets | No | The paper does not describe the use of any specific publicly available dataset, nor does it provide access information for any dataset. |
| Dataset Splits | No | The paper does not describe any experimental setup involving training, validation, or test dataset splits. |
| Hardware Specification | No | The paper is theoretical and does not describe any hardware specifications used for experiments. |
| Software Dependencies | No | The paper is theoretical and does not mention any software dependencies with specific version numbers. |
| Experiment Setup | No | The paper is theoretical and does not describe an experimental setup with specific hyperparameters or system-level training settings. |